This is a follow up question to this one.
Just to summarize. I want to find the kernel, eigenvalues and eigenvectors of the differential operator:
$$L(x):=x''+3x'-4x$$
In other words I want to find ...

Let $A$ be the operator $2(x+\partial_x)$. Suppose we have a function $f$ and that we apply the operator to this function. How this operator is applied? $2xf+\partial_xf$ or $2x+\partial_xf$? I guess ...

Let $\mathcal{O}$ be the ring of holomorphic functions on the unit disk deprived of the non-negative real numbers. Let $\mathcal{D}$ be the ring of differential operators on the same space, $\alpha$ a ...

While reading up on Sturm-Liouville system theory, I came across something I didn't fully understand. At one point, in the midst of proving the existence of solutions to the Sturm-Liouvill problem, ...

One of our teachers said that there is just one example that there is different between $(-(a\cdot b))$ and $((-a)\cdot b)$. He said by using "twice complement," you can find one.
I am trying to find ...

Some years ago I was in a lecture where I met for the first time the matrix representation of some differential and integral operators (once discretized). Back then, someone mentioned me that every ...

Suppose one is given with a sequence $S$ of non-negative real numbers $0\leq\lambda_0\leq \lambda_1\leq\dots\leq \lambda_n\leq\dots$. Under what conditions on $S$, is it possible to construct a Linear ...

The following is the general form of a linear ODE, where $t$ is the independent variable and $y$ is the dependent one:
$a_n(t) \frac{d^ny(t)}{dt^n} + a_{n-1}(t) \frac{d^{n-1}y(t)}{dt^{n-1}} + \dots + ...

I'm calculating the Christoffel symbols of the second kind which is of course defined as multiplying the symbol of the first kind multiplied by the contravariant metric. I was thinking of how to make ...

I have an expansion question using the $\nabla$. If I have this equation: $\nabla \dot\ (V \dot \ \nabla V)$. Where $V = x$ and $y$ components of velocity.
How does this expand to $(\frac{du}{dx})^2 ...

Let us assume that you have a volume form $\mu$ defined on a manifold $\mathcal{M}$. Then you can define the divergence operator with respect to this metric, such that the following relationship holds ...

The free Dirac operator is the differential operator of the following form
$$ T_0 = i \alpha \nabla + \beta,$$
where $\alpha$ and $\beta$ are Hermitian $4 \times 4$ matrices, and $T_0$ is selfadjoint ...

I have got a function $f=f(x)$. The derivative is $\partial_xf$. There are applications in which it is reasonable to treat $f$ as another variable in a larger context. In my application I now need an ...

I am currently reading this paper which makes use of generalized differential operators.
As I understood it, the operator $D_x$ works like this: If $F$ is a continuous function on $[a,b]$ and $G$ an ...

I work with the well known book of Dunford/Schwartz "Linear Operators (Part II)".
At first I should mention that the general difference between self-adjoint and symmetric operators is obvious to me. ...